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Proof step 4 from proof replay-lpt-at-above (previous step)

m < # lpt, n0 +1 < # lpt, n0 +1 ≤ m, ∀ lpt, m, nx. n0 < # lpt ∧ m < # lpt ∧ n0 ≤ m → replay-lpt(lpt, nx, n0)[m] = lpt[m] ⊦ replay-lpt(lpt, nx, n0 +1)[m] = lpt[m]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
n0 < # lpt, n0 < m, m < # lpt, n0 + 1 < # lpt, ∀ lpt, m, nx. n0 < # lpt ∧ m < # lpt ∧ n0 ≤ m → replay-lpt(lpt, nx, n0)[m] = lpt[m] ⊦ (lpt[n0].flags = LP_FREE ∨ n0 ∈ nx ⊃ replay-lpt(lpt, nx, n0) ;(lpt[n0].flags = LP_INDEX_NODES ∧ lpt[n0].ref-size ≠ 0 ⊃ replay-lpt(lpt, nx, n0)[n0, lpt[n0].size:= LEB_SIZE] ;(lpt[n0].ref-size = 0 ⊃ replay-lpt(lpt, nx, n0)[n0, mklp(0, 0, LP_FREE, lpt[n0].gcheapidx)];replay-lpt(lpt, nx, n0)) ) ) [m ] = lpt[m]

Rule argument

Additional information

Used simplifier rules: replay-lpt-rec: n < # lpt ⊦ replay-lpt(lpt, nx, n + 1) = (lpt[n].flags = LP_FREE ∨ n ∈ nx ⊃ replay-lpt(lpt, nx, n) ;(lpt[n].flags = LP_INDEX_NODES ∧ lpt[n].ref-size ≠ 0 ⊃ replay-lpt(lpt, nx, n)[n, lpt[n].size:= LEB_SIZE] ;(lpt[n].ref-size = 0 ⊃ replay-lpt(lpt, nx, n) [n, mklp(0, 0, LP_FREE, lpt[n].gcheapidx) ] ;replay-lpt(lpt, nx, n) ) ) );% ⊦ ¬ m + n < m; (s)% ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m +1 = m + 1; (s)